I am getting this error "Unknown property 'name' referenced in PageReference_Example_VF".

Can someone fix this, please?
Controller:

public class PageReference_Example {   
    public String selected {set;get;}
    public String name {set;get;}
    public PageReference callMe(){
        if(selected=='Housing'){
            PageReference p = new PageReference('/apex/HousingLoanPage');
            return p;
        }
        else{
            if(selected=='Personal'){
            PageReference p = new PageReference('/apex/PersonalLoanPage');
            return p;
        	}
        	else 
            	return null;
        }
    }
}

VF page

<apex:page controller="PageReference_Example">
    <apex:form>
    	<apex:page >
            <apex:pageBlock title="Home Page">
        		<apex:pageBlockSection >
            		<apex:pageBlockSectionItem>
                    	<apex:outputLabel value="Name"/>
                    	<apex:inputText value="{!name}"/>
                	</apex:pageBlockSectionItem>
            	</apex:pageBlockSection>
        	</apex:pageBlock>
        </apex:page>
    </apex:form>
</apex:page>

Hello Friends,

I am volunteering non profit organization, they have thier site in workpress, they would like to have form in Workpress and get volunteer request details in web to lead hrml form and create account in Lead object. I have generated Web to Lead form and it is working on our computer, but when we add the code to wordpress it is not working. 

It would be great help if you could guide me on this.

thanks